Abstract
A scheme for preparing vibrational SU(2) states of motion in a two-dimensional ion trap is described. These anticorrelated two-mode states are formally equivalent to the output photon states of a lossless SU(2) interferometer with number-state inputs. Nontrivial statistics such as the binomial distribution and the discrete ``arcsine'' distribution can be generated in the vibrational states of trapped ions, and detected by measuring the population inversion of the ion driven by a laser field along a specific direction. \textcopyright{} 1996 The American Physical Society.
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